Two matrix algorithms for eigenmodes of a Bessel-Gauss resonator

A Bessel-Gauss resonator (BGR) was proposed to produce the Bessel Gauss beams. In this paper transverse profiles and their corresponding losses of the BGR are computed by use of the entire matrix formalism and the transfer matrix method, and the computation results from two algorithms are compared. The computation results show that for the BGR there is no inconsistence in the mode fields yielded by two methods, and the transfer matrix methods are more accurate in the mode losses than the entire matrix formalism, which lead to a believable conclusion that the BGR with a convex-spherical mirror easily produces the fundamental Bessel-Gauss mode of good quality.     

Similarity Solutions for Generalized Variable Coefficients Zakharov-Kuznetsov Equation under Some Integrability Conditions

In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.     

Position calculation of the frequency band gap in the finite photonic crystal with multiple alternations using boundary element method

In this paper, the wave transmission from finite photonic crystals with multiple alternations is investigated using boundary element method (BEM). Since that, in these structures the alternation is not in all directions of space; the investigations of the frequency band gap with desired accuracy are not practical by analytical methods. Also, the frequency dispersion of dielectric rods is an effective parameter in photonic crystals, which this effect in our calculations has been considered. Due to the high capabilities of the BEM, the transmitted wave spectrum in the photonic crystal is calculated by changing the geometrical and optical parameters of the photonic crystal and applying more alternation in its structure and the position and width of the frequency band gap is investigated. Then, it is assumed that the photonic crystal with an arbitrary angle is rotated around the axis which is perpendicular on the crystal cross section and then, it is irradiated with a plan wave. The band gap of the photonic crystals with the desired structure, desired rotation angle and multiple alternations have been solved. Very low information volume, high speed and accuracy during the calculation and useable for any desired structures are the characteristics of this method.     

Mode Distribution and Bandwidth Characteristic of Arbitrarily Trapezoidal-Groove Guide for Millimeter Waves

The modes TE and TM of arbitrarily trapezoidal-groove guide are analyzed by using the mode-matching method. The mode TE₁₁ is the dominant mode of the trapezoidal-groove guide under different conditions. The bandwidth characteristic and the operation condition for the single dominant mode are discussed. The obtained conclusions are of very important significance in theoretical study and practical application of trapeziodal-groove guides for millimeter waves.     

Calculation of the Effect on the Reflection of the Plane Electromagnetic Wave for Non-Magnetized Plasma with Different Electron Density Distributions

In this paper, shift operator finite-difference time-domain (SO-FDTD) method is applied for the calculation of the dispersive medium. The high efficiency and accuracy of this method is verified by calculating the reflection of the plane electromagnetic wave impinging on a non-magnetized plasma slab with different electron density distributions. The results show that the average electron density only determines overall trends of the reflection, and different distributions affect the oscillating process of the reflection. If the average electron density maintains the same, the distribution of electron density with homogenous or inhomogeneous alternation will sharply take effects on the reflection. And magnitude of alternation of electron density affects the incident frequency directly when the reflection tends to uniform.     

The atomic structure and the properties of ununbium (<Emphasis Type="Italic">Z</Emphasis> = 112) and Mercury (<Emphasis Type="Italic">Z</Emphasis> = 80)

A super heavy element Uub (Z = 112) has been studied theoretically in conjunction with rela-tivistic effects and the effects of electron correlations. The atomic structure and the oscillator strengths of low-lying levels have been calculated, and the ground states have also been determined for the singly and doubly charged ions. The influence of relativity and correlation effects to the atomic properties of such a super heavy element has been investigated in detail. The results have been compared with the properties of an element Hg. Two energy levels at wave numbers 64470 and 94392 are suggested to be of good candidates for experimental observations.     

The magnetic properties of one-dimensional spin-1 ferromagnetic Heisenberg model in a magnetic field within Callen approximation

The effect of magnetic field h on the magnetic properties of the one-dimensional spin-1 ferromagnetic Heisenberg model is studied by the double-time Green’s function method. The magnetization and susceptibility are obtained within the Callen approximation. The zero-field susceptibility is as a decreasing function of the temperature T. The magnetization m increases in the whole field region, but the susceptibility maximum χ(T_m) decreases. The position T_m of the susceptibility maximum is both solved analytically and fits well to be a power law T_m∼h^γ at low fields and to be linear increasing at high fields. The height χ(T_m) decreases as a power law χ(T_m)∼h^−β with h increasing. The exponents (γ,β) obtained in our results agree with the other theoretical results. Our results are roughly in agreement with the results obtained in the experiment of Ni(OH)(NO₃)H₂O.     

Study of magnetotransport properties of interacting quantum dot systems using the ECA method

We study the magnetotransport of the interacting QD system in a magnetic field using the numerical method of embedded-cluster approximation (ECA). The spin-resolved conductances display different magnetic field dependences for different transport regimes. Through comparison of conductance polarization, the mixed-valence regime shows the largest polarization. The spin-resolved conductance as a function of the ratio between the magnetic field and Kondo temperature H/TK is found to exhibit an approximate universal behavior in the Kondo regime. We also investigate conductance dependence on interaction strength and find interesting inversion of sign of polarization in some cases.     

Analysis of the radiative transfer equation with highly assymetric phase function

This paper considers a scalar radiative transfer problem with high scattering anisotropy. Two computational methods are presented based on decomposition of the diffuse light field into a regular and anisotropic part. The first algorithm (DOMAS) singles out the anisotropic radiance in the forward scattering peak using the Small-Angle Modification of RTE. The second algorithm (DOM2+) separates the single scattering radiance as an anisotropic part, which largely defines the fine detail of the total radiance in the backscattering directions. In both cases, the anisotropic part is represented analytically. With anisotropy subtraction, the regular part of the signal, which requires a numerical solution, is essentially smoothed as a function of angles. Further, the transport equation is obtained for the regular part that contains an additional source function from the anisotropic part of the signal. This equation is solved with the discrete ordinates method. A conducted numerical analysis of this work showed that algorithm DOMAS has a strong advantage as compared to the standard discrete ordinates method for simulation of the radiance transmission, and DOM2+ is the best of the three for the reflection computations. Both algorithms offer at least a factor of three acceleration of convergence of the azimuthal series for highly anisotropic phase functions.